Seminars and Colloquia by Series

Tuesday, November 25, 2008 - 15:00 , Location: Skiles 269 , Nizar Demni , University of Bielefeld , Organizer: Heinrich Matzinger
We will introduce the Dunkl derivative as well as the Dunkl process and some of its properties. We will treat its radial part called the radial Dunkl process and light the connection to the eigenvalues of some matrix valued processes and to the so called Brownian motions in Weyl chambers. Some open problems will be discussed at the end.
Monday, November 24, 2008 - 14:00 , Location: Skiles 255 , Ignacio Uriarte-tuero , Michigan State University , Organizer: Michael Lacey
In his celebrated paper on area distortion under planar quasiconformal mappings (Acta 1994), K. Astala proved that a compact set E of Hausdorff dimension d is mapped under a K-quasiconformal map f to a set fE of Hausdorff dimension at most d' = \frac{2Kd}{2+(K-1)d}, and he proved that this result is sharp. He conjectured (Question 4.4) that if the Hausdorff measure \mathcal{H}^d (E)=0, then \mathcal{H}^{d'} (fE)=0. This conjecture was known to be true if d'=0 (obvious), d'=2 (Ahlfors), and more recently d'=1 (Astala, Clop, Mateu, Orobitg and UT, Duke 2008.) The approach in the last mentioned paper does not generalize to other dimensions. Astala's conjecture was shown to be sharp (if it was true) in the class of all Hausdorff gauge functions in work of UT (IMRN, 2008). Finally, we (Lacey, Sawyer and UT) jointly proved completely Astala's conjecture in all dimensions. The ingredients of the proof come from Astala's original approach, geometric measure theory, and some new weighted norm inequalities for Calderon-Zygmund singular integral operators which cannot be deduced from the classical Muckenhoupt A_p theory. These results are intimately related to (not yet fully understood) removability problems for various classes of quasiregular maps. The talk will be self-contained.
Monday, November 24, 2008 - 14:00 , Location: Skiles 269 , Sa'ar Hersonsky , University of Georgia , Organizer: John Etnyre
Cannon: "A f.g. negatively curved group with boundary homeomorphic to the round two sphere is Kleinian". We shall outline a combinatorial (complex analysis motivated) approach to this interesting conjecture (following Cannon, Cannon-Floyd-Parry). If time allows we will hint on another approach (Bonk-Kleiner) (as well as ours). The talk should be accessible to graduate students with solid background in: complex analysis, group theory and basic topology.
Series: PDE Seminar
Friday, November 21, 2008 - 16:05 , Location: Skiles 255 , Athanasios Tzavaras , Univeristy of Maryland , Organizer:
We consider a system of hyperbolic-parabolic equations describing the material instability mechanism associated to the formation of shear bands at high strain-rate plastic deformations of metals. Systematic numerical runs are performed that shed light on the behavior of this system on various parameter regimes. We consider then the case of adiabatic shearing and derive a quantitative criterion for the onset of instability: Using ideas from the theory of relaxation systems we derive equations that describe the effective behavior of the system. The effective equation turns out to be a forward-backward parabolic equation regularized by fourth order term (joint work with Th. Katsaounis and Th. Baxevanis, Univ. of Crete).
Friday, November 21, 2008 - 15:00 , Location: Skiles 255 , Nick Zhao , University of Central Florida , Organizer: Prasad Tetali
In 1968, Vizing proposed the following conjecture which claims that if G is an edge chromatic critical graph with n vertices, then the independence number of G is at most n/2. In this talk, we will talk about this conjecture and the progress towards this conjecture.
Friday, November 21, 2008 - 14:00 , Location: Skiles 269 , Ken Baker , University of Miami , Organizer: John Etnyre
Lickorish observed a simple way to make two knots in S^3 that produced the same manifold by the same surgery. Many have extended this result with the most dramatic being Osoinach's method (and Teragaito's adaptation) of creating infinitely many distinct knots in S^3 with the same surgery yielding the same manifold. We will turn this line of inquiry around and examine relationships within such families of corresponding knots in the resulting surgered manifold.
Thursday, November 20, 2008 - 15:00 , Location: Skiles 269 , Jian-Jian Ren , Department of Mathematics, University of Central Florida , Organizer: Heinrich Matzinger
So far, likelihood-based interval estimate for quantiles has not been studied in literature for interval censored Case 2 data and partly interval-censored data, and in this context the use of smoothing has not been considered for any type of censored data. This article constructs smoothed weighted empirical likelihood ratio confidence intervals (WELRCI) for quantiles in a unified framework for various types of censored data, including right censored data, doubly censored data, interval censored data and partly interval-censored data. The 4th-order expansion of the weighted empirical log-likelihood ratio is derived, and the 'theoretical' coverage accuracy equation for the proposed WELRCI is established, which generally guarantees at least the 'first-order' accuracy. In particular for right censored data, we show that the coverage accuracy is at least O(n^{-1/2}), and our simulation studies show that in comparison with empirical likelihood-based methods, the smoothing used in WELRCI generally gives a shorter confidence interval with comparable coverage accuracy. For interval censored data, it is interesting to find that with an adjusted rate n^{-1/3}, the weighted empirical log-likelihood ratio has an asymptotic distribution completely different from that by the empirical likelihood approach, and the resulting WELRCI perform favorably in available comparison simulation studies.
Thursday, November 20, 2008 - 12:05 , Location: Skiles 255 , Carl Yerger , School of Mathematics, Georgia Tech , Organizer: Robin Thomas
Given a configuration of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex, and the placement of one of these on an adjacent vertex. The pebbling number of a graph G is the smallest integer k such that given any configuration of k pebbles on G and any specified vertex v in V(G), there is a sequence of pebbling moves that sends a pebble to v. We will show that the pebbling number of a graph of diameter four on n vertices is at most 3n/2 + O(1), and this bound is best possible up to an additive constant. This proof, based on a discharging argument and a decomposition of the graph into ''irreducible branches'', generalizes work of Bukh on graphs of diameter three. Further, we prove that the pebbling number of a graph on n vertices with diameter d is at most (2^{d/2} - 1)n + O(1). This also improves a bound of Bukh.
Thursday, November 20, 2008 - 11:00 , Location: Skiles 255 , Dmitriy Bilyk , IAS & U South Carolina , Organizer: Michael Lacey

Note change in time.

The theory of geometric discrepancy studies different variations of the following question: how well can one approximate a uniform distribution by a discrete one, and what are the limitations that necessarily arise in such approximations. Historically, the methods of harmonic analysis (Fourier transform, Fourier series, wavelets, Riesz products etc) have played a pivotal role in the subject. I will give an overview of the problems, methods, and results in the field and discuss some latest developments.
Wednesday, November 19, 2008 - 13:30 , Location: ISyE Executive Classroom , Lei Wang , ACO Student, School of Mathematics, Georgia Tech , Organizer: Annette Rohrs
Nash bargaining was first modeled in John Nash's seminal 1950 paper. In his paper, he used a covex program to give the Nash bargaining solution, which satifies many nature properties. Recently, V.Vazirani defined a class of Nash bargaining problem as Uniform Nash Bargaining(UNB) and also defined a subclass called Submodular Nash Bargaining (SNB). In this talk, we will consider some game theoretic issues of UNB: (1) price of bargaining; (2) fully competitiveness; (3) min-max and max-min fairness and we show that each of these properties characterizes the subclass SNB.

Pages